Two engineers are having an argument about the efficiency of a tube-side multipass heat exchanger compared to a similar exchanger with a single tube-side pass. Smith claims that for a given number of tubes and rate of heat transfer, more area is required in a two-pass exchanger than in a one-pass, because the effective temperature difference is less. Jones, on the other hand, claims that because the tube-side velocity and hence coefficient is higher, less area is required in a two-pass exchanger. With the conditions given below, which engineer is correct? Which case would you recommend, or what changes in the exchanger would you recommend?
Exchanger specifications
– 200 tube passes total
– 1 in.-O.D copper tubes, 16 B.W.G.
Tube-side fluid
Water entering at 16°C, leaving at 28°C, with a rate of 225,000 kg/h.
Shell-side fluid
Mobiltherm 600, entering at 50°C, leaving at 33°C.
Shell side coefficient = 1700 W/(m2 K)
GIVEN
• Tube and shell heat exchanger - water in tubes, Mobiltherm 600 in shell
• Number of tube passes (Np) = 200
• Tubes are 1 in copper 16 B.W.G.
• Water flow rate m w= 225,000 kg/h = 62.5 kg/s
• Water temperatures
? Tw,in = 16°C
? Tw,out = 28°
• Mobiltherm temperatures
? Tm,in = 50°C
? Tm,out = 33°C
• Shell side heat transfer coefficient h o= 1700 W/(m2 K)
FIND
• Which required less transfer area: (a) single tube pass (b) Two tube passes?
ASSUMPTIONS
• Thermal resistance of copper tube wall is negligible
SKETCH
PROPERTIES AND CONSTANTS
for 1 in 16 B.W.G. tubes, the diameters are
Di = 0.870 in. = 0.0221 m
Do = 1.0 in. = 0.0254 m
for water at the average temperature of 22°C
Thermal conductivity (k) = 0.601 W/(m K)
Kinematic viscosity (?) = 0.957 × 10–6 m2/s
Prandtl number (Pr) = 6.6
Density (?) = 998 kg/m3
Specific heat (cpw) = 4180 J/(kg K)
the specific heat of Mobiltherm 600 at its average temperature of 42°C (cpm) = 1654 J/(kg K)
For case (a) number of flow passages (N) = Total passes/(passes per tube) = 200/1 = 200.
For case (b) N = 200/2 = 100.
The water velocity (V) is determined by
The Reynolds number is
The Nusselt number for turbulent flow in a tube is
The overall heat transfer coefficient, neglecting the tube wall resistance is
Case (a)
Case (b)
The Log-mean temperature difference for counterflow, is
For case (a): ?Tmean = LMTD = 19.4°C
For case (b): The LMTD must be corrected
F = 0.91
The rate of heat transfer is
Case (a)
Case (b)
COMMENTS
For these operating conditions, the double-pass heat exchanger requires about 8% less area because although the mean temperature difference for the double pass is 9% less than that for the single pass, the overall heat transfer coefficient is 18% greater.
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